Ford has had a very odd brake light switch design for a long time. There is no adjustment possible or needed. If it takes too long to turn on most likely the contacts inside are pitted or arced. Replacing the switch will solve the problem.

The other possibility is broken wires going to the switch. Because it is attached to and moves back and forth with the brake pedal, the wires are constantly flexing. There could be an intermittent break that makes a temporary connection when the pedal moves far enough. To check for that before you replace the switch, use a small jumper wire to connect the two terminals on the switch without pushing on the brake pedal. If the brake lights do not come on, flex the wires a little. If that makes the lights flicker on, repair the wires instead of replacing the switch.